Logical and arithmetic circuits in Belousov-Zhabotinsky encapsulated disks

Abstract

Excitation waves on a subexcitable Belousov-Zhabotinsky (BZ) substrate can be manipulated by chemical variations in the substrate and by interactions with other waves. Symbolic assignment and interpretation of wave dynamics can be used to perform logical and arithmetic computations. We present chemical analogs of elementary logic and arithmetic circuits created entirely from interconnected arrangements of individual BZ encapsulated cell-like disk. Interdisk wave migration is confined in carefully positioned connecting pores. This connection limits wave expansion and unifies the input-output characteristic of the disks. Circuit designs derived from numeric simulations are optically encoded onto a homogeneous photosensitive BZ substrate.

Chemical computing with reaction–diffusion processes

“…In a series of recent papers, Adamatzky and co-workers considered the logic gates, as well as some selected arithmetic operations, executed by a system of sub-excitable discs [34,[43][44][45][46]. Their simulation results were supported by experiments with Ru-catalysed BZ reaction in which the catalyst was immobilized on a membrane and the membrane was placed in a solution of the other reagents of BZ reaction [46]. Areas of low-intensity illumination formed sub-excitable interiors of discs.…”

Information coding with frequency of oscillations in Belousov-Zhabotinsky encapsulated disks

“…Let us consider a medium composed of dark disks on illuminated background. The medium is very similar to that studied in [17,18,19,20,21], but in these papers dark disks were sub-excitable, whereas here the medium inside dark disks is oscillatory. As an experimental realization of such medium one can use a membrane with immobilised catalyst of photosensitive BZ that is placed inside a solution of the other reagents [29].…”

“…For the simplest applications, where the number of connections between objects can be restriced to a few, 2-D disks seem to be as good 3-D droplets. It can be shown that the basic informa- tion processing devices can be constructed with excitable disks with precisely controlled excitability level and coding based on the presence of excitation pulses [17,18,19,20,21]. However, the recent experiments performed within the NEUNEU project [24] have shown that it is relatively easy to prepare a structure composed of interacting droplets containing oscillatory BZ medium separated by a non-oscillatory oil phase [23].…”

“…The ratio of time scales for the evolution of Experiments with lipid covered BZ droplets have shown that high frequency oscillations expand between droplets like excitation spikes. Therefore, we can expect that structures of disks for processing information coded in frequency of local oscillations are similar to those that process information coded in the presence of excitation pulses [17,18,19,20,21]. Fig.…”

“…In the series of recent papers Adamatzky and collaborators [17,18,19,20,21] considered the logic gates as well as some selected arithmetic operations executed by a system of sub-excitable disks. Their numerical simulations were based on the Oregonator model for a photosensitive BZ reaction [22].…”